Physics: CUET Mock Test - 5 - CUET MCQ

Given: E_rms = 300 V
The required equation is → P.I.V. = 2 × E₀ or P.I.V. = 2√2 × E_rms
P.I.V. = 2√2 × 300 V
P.I.V. = 848.52 V ≈ 849 V.

Concept:

The photoelectric effect:

• The photoelectric effect is the phenomenon where electrons are emitted from the surface of a metal when radiation of appropriate frequency, such as visible or ultraviolet light, is allowed to incident on it.
• This effect was first observed by Heinrich Hertz in 1887 and was later explained by Albert Einstein in 1905.
• In the photoelectric effect, a photon of sufficient energy strikes the metal's surface, transferring its energy to an electron in the metal.
• If the photon's energy is greater than the metal's work function, which is the minimum energy required to remove an electron from the metal, the electron can be ejected from the metal's surface.

Application:

The photoelectric effect has many practical applications, including photovoltaic cells used in solar panels, photoelectric detectors used in cameras, and photocells used in automatic doors and burglar alarms.

Additional InformationNuclear fission:

• Nuclear fission is the process where the nucleus of an atom is split into smaller nuclei, releasing a large amount of energy.
• This process is used in nuclear power plants to generate electricity.

Compton effect:

• The Compton effect is the phenomenon where a photon loses some of its energy when it collides with an electron, resulting in the photon's wavelength increasing.
• This effect is used in medical imaging to produce X-ray images of the body.

Thermionic emissions:

• Thermionic emissions are the emissions of electrons from heated material.
• This process is used in electron guns to produce the electrons used in cathode ray tubes and vacuum tubes.

The correct answer is option (3)

Concept:

De Broglie wavelength:

• The De Broglie wavelength is given by the formula λ = h/p---(1)

where h is Planck's constant and p is the momentum of the particle.

• Since all the particles have the same kinetic energy, we can say that they all have the same momentum, as momentum is given by p = √(2mK), where m is the mass of the particle and K is the kinetic energy.

Now, comparing the masses of the particles

We can see that the α particle (which consists of two protons and two neutrons) has the largest mass, followed by the deuteron (which consists of a proton and a neutron), then the proton, and finally the electron with the smallest mass.

Since for the same kinetic energy K, the de Broglie wavelength is inversely proportional to the square root of the mass.

Out of the given particles, the alpha particle has the highest mass and would possess De Broglie wavelength.

The correct answer is option (3)

Concept:
The ratio of radii of two nuclei can be approximated by the following formula:

Where r₁ and r₂ are the radii of the two nuclei, and A₁ and A₂ are their atomic mass numbers.
Using this formula, we can calculate the ratio of radii of the two nuclei with atomic mass numbers 27 and 8 respectively as follows:

Therefore, the ratio of radii of the two nuclei is 1.5 i.e. 3/2.
The correct answer is option (1)

Important Points

• This formula is based on the assumption that the nuclear density is constant for both nuclei.
• It is derived from the fact that the volume of a nucleus is proportional to its mass number, and the radius of a nucleus is proportional to the cube root of its volume.
• However, it should be noted that this formula is only an approximation and may not hold true for all nuclei.

Calculation:

The amount of substance left after 12 years can be found using the formula for radioactive decay:

N(t) = No * (1/2)​(t/t_1/2)

where N(t) is the amount of substance remaining after time t, No is the original amount of substance, t_1/2 is the half-life, and t is the time elapsed.

In this case, No (since No is the original mass), t1/2 = 4 years, and t = 12 years.

Substituting these values into the formula gives:

N(12) = No * (1/2)^12/4
N(12) = No * (1/2)³
N(12) = N_o/8
N(12) = 0.125 * No

Therefore, after 12 years, the amount of substance remaining is 0.125 times the original mass or 12.5% of the original mass.

N = N0/8

The correct answer is option (3)

Concept:

Uranium:

• Uranium is a radioactive element commonly used as fuel in nuclear reactors. It can undergo nuclear fission, releasing a large amount of energy.
• The rate of the fission reaction can be controlled by adjusting the concentration of Uranium-235, a fissile isotope of uranium, in the fuel rods.
• It is used for fission reactions.

Moderator:

• In a nuclear reactor, the fission reaction produces fast-moving neutrons that need to be slowed down in order to interact with the fuel and sustain the reaction.
• The moderator is a material, usually water or graphite, that is used to slow down the neutrons to a speed at which they can interact with the fuel and produce more neutrons.
• It Slows down the fast-moving neutrons

Control rod:

• Control rods are devices made of neutron-absorbing materials such as boron or cadmium that can be inserted or removed from the reactor core to control the rate of the fission reaction.
• By absorbing neutrons, the control rods reduce the number of neutrons available to interact with the fuel, slowing down or stopping the reaction.
• The reaction rate can be controlled by it.

Coolant:

• The coolant is a fluid, typically water or gas, that circulates through the reactor core to transfer heat from the fuel rods to a steam turbine.
• The heat generated by the fission reaction is used to produce steam, which drives the turbine and generates electricity.
• The coolant also helps to regulate the temperature of the core and prevent it from overheating.
• It transfers heat from the core to turbine.

​So, the answer would be (A) - (III), (B) - (II), (C) - (I), (D) - (IV)

The correct answer is option (3).

Concept:

The intensity of a sinusoidal plane electromagnetic wave defined as the average value of poynting vector taken over one cycle (in free space)

I = P_av/(4πr²) = E_m²/2μ₀c

Where,

Pav → Average power

Em → Maximum value of electric field

r → Distance

μ0 → permeability of free space = 4π × 10^-7 m kg s^-2 A^-2

c → Speed of light = 3 × 10⁸ m/s

Calculation:

Given

Pav = 1000 W

r = 3.5 m

μ0 = 4π × 10-7 m kg s-2 A-2

c = 3 × 108 m/s

Pav/(4πr2) = Em2/2μ0c

⇒ Em = √[2μ0cPav/(4πr2)]

∴ Em = √[4π × 10-7 ×3 × 108× 1000/(2π3.52)]

=69.98 ≈ 70 V/m

Statement I is correct because refraction happens due to a change in the speed of light as it moves from one transparent medium to another.

Statement II is also correct as the refractive index of water is approximately 1.33.

The correct answer is option 3):(1500 C)

Concept:

If Q charge flows through the conductor for ‘t’ seconds, then the current given by that conductor is

I=

Q = I × t

I = current

t = time

Calculation:

Given

I = 5 A

t = 5 min = 300 sec

Q = 5× 300

= 1500 C

Concept:

• The refractive index, also called the index of refraction, measures the bending of a ray of light when passing from one medium into another.
• Also defined as the ratio of the speed of light in a vacuum to the speed of light in a medium.
• The refractive index of a medium can be calculated using the following formula:
• n = c/v
• where n is the refractive index of the medium, c is the velocity of light in vacuum, and v is the velocity of light in the medium.
• Lens maker formula.
• 

Explanation:

Let the refractive index of the medium is n₁.

• The refractive index of the liquid must be equal to 1.47 in order to make the lens disappear.
• This means n₁ = n.
• From lens maker formula.
• This gives 1/f = 0 or f → ∞.
• The lens in the liquid will act like a plane sheet of glass.
• The liquid could be glycerine.

Assertion (A): A magician during a show makes a glass lens with n = 1.47 disappear in a trough of liquid.

Reason (R): The refractive index of the liquid must be equal to 1.47 in order to make the lens disappear.

• A is correct because the lens vanishes when the refractive index of the surrounding liquid matches that of the lens.
• R is also correct as it explains why the lens appears to disappear—when the refractive indices are equal, light does not refract at the interface, making the lens invisible.
• The correct choice is B: both A and R are correct, and R provides the correct explanation for A.

Total current through the wire is given by:

I = ∫₀^R J(r)·2πr dr

Substitute the given current density:

I = ∫₀^R J₀ (1 − r²/R²) · 2πr dr

Take constants outside the integral:

I = 2πJ₀ ∫₀^R (1 − r²/R²) r dr

Split the integral:

I = 2πJ₀ [ ∫₀^R r dr − (1/R²) ∫₀^R r³ dr ]

Evaluate the integrals:

∫₀^R r dr = R²/2,    ∫₀^R r³ dr = R⁴/4

Substitute the values:

I = 2πJ₀ [ R²/2 − R²/4 ] = 2πJ₀ · R²/4 = πJ₀R²/2

Final Answer: I = πJ₀R²/2

Voltage across 5Ω=10 V

∴ I = 10/5 A = 2 A

The electrons in a conductor have random velocities and when an electric field is applied, they suffer repeated collisions and in the process move with a small average velocity, opposite to the direction of the field. This is equivalent to positive charge flowing in the direction of the field.

As charges and velocities are same
F=q(V×B)
So having the same magnitude of charge and same velocity, they'll experience the same magnitude of force.

The correct answer would be option B. Applying a very strong magnetic field.
Applying a very strong magnetic field to a metal we don’t know the electron emission.

A photon of wavelength 6000 nm collides with an electron at rest. After scattering, the wavelength of the scattered photon is found to change by exactly one Compton wavelength.

Frequency=C/ λ
λ=h/P
frequency=C P/ h
f=(3×10⁸×3.3×10^-29)/6.6×10^-34
f=3× 10¹³/2
f=1.5×10¹³ Hz

Φ= hνλ => 2eV= 6.626 x 10^-34 x ν

2 x 1.6 x 10^-19= 6.626 x 10^-34 x ν

On solving we get ν = 4.6 x 10¹⁴ Hz.

Though water and ammonia are covalent molecules, they have a net dipole moment due to their distorted structure than the ideal one. Hydrochloric acid has a linear molecular structure but its net dipole moment is towards the Hydrogen atom. But methane has a symmetrical tetrahedral structure and its net dipole moment is zero hence it doesn’t behave as a permanent dipole. Methane solvents are therefore non-polar solvents.

We know k = 1 (given)
Force on a unit point charge kept at a distance r from the charge = q/r². Therefore, work done to bring that point charge through a small distance dr =(q/(r²)) * (-dr). Therefore, the potential of that point is =

When the frequency of an ac is doubled → The inductive reactance (X_L) gets doubled.
This is because inductive reactance is directly proportional to the frequency of an alternating current circuit.

For a step-up transformer, the voltage at the second terminal is greater than the primary terminal, i.e. → V_s > V_p. Similarly, the current in the secondary coil is lesser than that current flowing the primary coil, i.e. → I_s < I_p. Also, the number of turns in the secondary winding is greater than that in the primary winding, i.e. → N_s > N_p. So the transformation ratio will be greater than 1. So, the correct combination is given as:
k > 1; V_s > V_p, I_s < I_p, N_s > N_p

f = X_L/2πL
f = 3500/(2×3.14×2.5)
f = 222.9 Hz ≈ 223 Hz
Therefore, the frequency of a coil having reactance of 3500 Ω is 223 Hz.

Original fringe width is given as → β = Dλ/d.
So, the new fringe width is → β’ = 
β’ = 4β
Therefore, the new fringe width is 4 β.

Angular magnification is maximum when the final image is formed at the near point.

u = -7.1 cm.
Therefore, the object should be placed 7.1 cm before the lens to avoid angular magnification.

Given: I₀ = 0.092 A
The required equation is → I_rms = I_o/√2
I_rms = 0.092/1.414
I_rms = 0.065 A

N = N₀e^{-(λ1 + λ2) t}.
4 = e^{(λ1 + λ2) t}.
t =  = 1080 year.